Can someone help me find out when the population of the city will reach 140 thousand? Thanks!

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Answer 1 · 2018-01-14T11:36:20

#color(blue)(2005)# to the nearest year.

You already have the formula #A=118e^(0.024t)#.

Since #A# is the amount after t years, we have:

#140=118e^(0.024t)#

The amount is in thousands, so 140=140,000

Now we solve for #t#:

Divide by #118#

#140=118e^(0.024t)#

#70/59=e^(0.024t)#

Take natural logs of both sides:

#ln(70/59)=0.024tln(e)#

#ln(e)=1#

#:.#

#ln(70/59)=0.024t#

Divide by #0.024#

#(ln(70/59))/0.024=t#

Evaluate for #t#:

#t=(ln(70/59))/0.024=7.123241592#

We started in 1998, so t years after this period:

#1998+7.123241592=2005.123242#

#color(blue)(2005)# to the nearest year.